Cellular automata as discrete computational schemes can be used to model and understand the time evolution of physical processes. We show a cellular automata rotating polar grid that can be used as a galaxy construction and evolution scheme. This model shows structure matching the morphology of spiral galaxies using inputs such as star formation site size, rate, and galaxy rotation. Grids with large numbers of cells can be run rapidly, allowing for fast exploration of the parameter space. We also describe our methods for visualizing the constructed models.